The field of the invention is magnetic resonance imaging (“MRI”) methods and systems. More particularly, the invention relates to the generation of spatially-tailored excitation pulses for parallel transmission MRI systems.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mxy. A signal is emitted by the excited nuclei or “spins”, after the excitation signal B1 is terminated, and this signal may be received and processed to form an image.
When utilizing these “MR” signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The measurement cycle used to acquire each MR signal is performed under the direction of a pulse sequence produced by a pulse sequencer. Clinically available MRI systems store a library of such pulse sequences that can be prescribed to meet the needs of many different clinical applications. Research MRI systems include a library of clinically proven pulse sequences and they also enable the development of new pulse sequences.
The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space”. Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. Most pulse sequences sample k-space in a raster scan-like pattern sometimes referred to as a “spin-warp”, a “Fourier”, a “rectilinear”, or a “Cartesian” scan. The spin-warp scan technique employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of MR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (“2DFT”), for example, spatial information is encoded in one direction by applying a phase encoding gradient, Gy, along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient, Gx, in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT pulse sequence, the magnitude of the phase encoding gradient pulse, Gy, is incremented, ΔGy, in the sequence of measurement cycles, or “views” that are acquired during the scan to produce a set of k-space MR data from which an entire image can be reconstructed.
There are many other k-space sampling patterns used by MRI systems These include “radial”, or “projection reconstruction” scans in which k-space is sampled as a set of radial sampling trajectories extending from the center of k-space. The pulse sequences for a radial scan are characterized by the lack of a phase encoding gradient and the presence of a readout gradient that changes direction from one pulse sequence view to the next. There are also many k-space sampling methods that are closely related to the radial scan and that sample along a curved k-space sampling trajectory rather than the straight line radial trajectory.
An image is reconstructed from the acquired k-space data by transforming the k-space data set to an image space data set. There are many different methods for performing this task and the method used is often determined by the technique used to acquire the k-space data. With a Cartesian grid of k-space data that results from a 2D or 3D spin-warp acquisition, for example, the most common reconstruction method used is an inverse Fourier transformation (“2DFT” or “3DFT”) along each of the 2 or 3 axes of the data set. With a radial k-space data set and its variations, the most common reconstruction method includes “regridding” the k-space samples to create a Cartesian grid of k-space samples and then perform a 2DFT or 3DFT on the regridded k-space data set. In the alternative, a radial k-space data set can also be transformed to Radon space by performing a 1DFT of each radial projection view and then transforming the Radon space data set to image space by performing a filtered backprojection.
Depending on the technique used, many MR scans currently used to produce medical images require many minutes to acquire the necessary data. The reduction of this scan time is an important consideration, since reduced scan time increases patient throughout, improves patient comfort, and improves image quality by reducing motion artifacts. Many different strategies have been developed to shorten the scan time.
One such strategy is referred to generally as “parallel imaging”. Parallel imaging techniques use spatial information from arrays of RF receiver coils to substitute for the encoding that would otherwise have to be obtained in a sequential fashion using RF pulses and field gradients (such as phase and frequency encoding). Each of the spatially independent receiver coils of the array carries certain spatial information and has a different sensitivity profile. This information is utilized in order to achieve a complete location encoding of the received MR signals by a combination of the simultaneously acquired data received from the separate coils. Specifically, parallel imaging techniques undersample k-space by reducing the number of acquired phase-encoded k-space sampling lines while keeping the maximal extent covered in k-space fixed. The combination of the separate MR signals produced by the separate receiver coils enables a reduction of the acquisition time required for an image (in comparison to conventional k-space data acquisition) by a factor that in the most favorable case equals the number of the receiver coils. Thus the use of multiple receiver coils acts to multiply imaging speed, without increasing gradient switching rates or RF power.
Most MRI scanners use a single-channel RF excitation coil to tip the spin magnetization away from its equilibrium state and initiate a measurement cycle. Usually, an RF excitation pulse is used to excite either all of the spins inside the excitation coil (non-selective excitation), a single slice through the subject (slice-selective excitation), or within only a specific region, such as, a small cube (3-D spatially-selective excitation). In spatially-selective, spatially-tailored excitation, the RF pulse is played out in the presence of gradient waveforms that impart a gradient onto the main magnetic field of the MRI system, which is instrumental in the spatial and selective excitation process. In general, the gradient field may be viewed as causing the traversal of a curve in excitation k-space, a path that may proceed through all three dimensions of k-space (kx, ky, and kz), which under certain assumptions is essentially a 3D Fourier domain. During this traversal of excitation k-space, the energy of the RF pulse being played in conjunction with the gradient waveforms may be viewed as depositing RF energy along this k-space excitation trajectory curve. The RF pulse thus produces an excitation that modulates (in phase, in amplitude, or both) as a function of position (kx, ky, and kz) in excitation k-space. The resulting excitation is often closely related to the inverse Fourier transform of this deposited energy.
For example, in a typical slice-selective RF pulse, a constant gradient field is applied in the z-direction while an RF pulse shaped like a sine cardinal (“sinc”) function is transmitted through the MRI system's single excitation coil. In this instance, the gradient field causes the RF pulse energy to be deposited along a single line (a “spoke”) in the kz-direction of excitation k-space, that is, a line through the k-space position (0,0,kz). This sinc-like deposition in kz excites only those magnetic spins within a thin slice of tissue due to the Fourier relationship between energy deposited in excitation k-space and the flip angle of the resulting magnetization. In short, the magnetization that results from this typical RF pulse is a constant degree of excitation within the slice and no excitation out of the slice.
Recent work has extended this slice-selective concept to all three spatial dimensions, in which not only a thin slice is excited, but a particular pattern within the slice itself is excited. These “spatially-tailored” excitations in 2D and 3D require lengthy application of the RF excitation and associated gradients. A recent method, termed “parallel transmission” (and sometimes referred to as “parallel excitation”), exploits variations among the different spatial profiles of a multi-element RF coil array. This permits sub-sampling of the gradient trajectory needed to achieve the spatially-tailored excitation and this method has been shown in many cases to dramatically speed up, or shorten, the corresponding RF pulse.
This “acceleration” of the spatially-tailored RF excitation process makes the pulse short enough in duration to be clinically useful. Accelerations of 4 to 6 fold have been achieved via an 8 channel transmit system as disclosed by K. Setsompop, et al., in “Parallel RF Transmission with Eight Channels at 3 Tesla,” Magnetic Resonance in Medicine; 2006, 56:1163-1171. This acceleration enables several important applications, including flexibly-shaped excitation volumes and mitigation of RF field inhomogeneity at high field for slice or slab-selective pulses. A number of methods have been proposed for the design of the RF and gradient waveforms for parallel excitation, such as those disclosed, for example, by U. Katscher, et al., in “Transmit SENSE,” Magnetic Resonance in Medicine; 2003, 49:144-150; by Y. Zhu in “Parallel Excitation with an Array of Transmit Coils,” Magnetic Resonance in Medicine; 2004, 51:775-784; by M. Griswold, et al., in “Autocalibrated Accelerated Parallel Excitation (Transmit-GRAPPA),” Proceedings of the 13th Annual Meeting of ISMRM; 2005, 2435; and by W. Grissom, et al., in “Spatial Domain Method for the Design of RF Pulses in Multicoil Parallel Excitation,” Magnetic Resonance in Medicine; 2006, 56:620-629.
Successful implementations have been demonstrated on multi-channel hardware, including those described by P. Ullmann, et al., in “Experimental Analysis of Parallel Excitation Using Dedicated Coil Setups and Simultaneous RF Transmission on Multiple Channels,” Magnetic Resonance in Medicine; 2005, 54:994-1001; by D. Xu, et al., in “A Noniterative Method to Design Large-Tip-Angle Multidimensional Spatially-Selective Radio Frequency Pulses for Parallel Transmission,” Magnetic Resonance in Medicine; 2007, 58:326-334; and by P. Vernickel, et al., in “Eight-Channel Transmit/Receive Body MRI Coil at 3 T,” Magnetic Resonance in Medicine; 2007, 58:381-389.
In conventional pulse design, a general excitation format is selected, such as a slice-selective excitation, and a standard set of gradients and a radiofrequency (“RF”) pulse are chosen to accomplish the desired effect. For example, and as mentioned above, a constant gradient field is applied in the z-direction while an RF pulse shaped like a sine cardinal (“sinc”) function is transmitted through the MRI system's single excitation coil to excite a thin slice of tissue along the spatial z-direction. Cases such as this are one of the simplest examples of pulse design. An extension of this example is where an excitation k-space trajectory is selected first. For example, if a highly structured two-dimensional (“2D”) pattern needs to be excited, the MRI operator may choose a set of gradient waveforms that cause a 2D pattern echo-planar or spiral trajectory to be traversed in excitation space (kx,ky). Exemplary patterns of such k-space trajectories are shown in FIGS. 1A and 1B, respectively.
If a parallel transmission system is available, the trajectory may be “accelerated” by undersampling it and using, for example, a shorter echo-planar or spiral sampling trajectory. Only after deciding upon the excitation k-space trajectory and gradients does the MRI operator proceed to design an RF pulse to accompany and deposit energy along the trajectory. In other words, the RF pulse is automatically optimized based on the desired target excitation pattern, but the excitation k-space trajectory is not.
Recently, researchers have begun to branch away from the conventional design approaches discussed above and have developed methods that attempt to jointly design both the excitation k-space trajectory and the RF excitation pulse, while optimizing both concurrently. These methods are similar in that they provide a desired target excitation pattern and then, in some manner, search over numerous trajectories, or types of trajectories. In this manner, they proceed to find a “trajectory-pulse” pair that produces a version of the trajectory and resulting excitation that satisfy some predefined constraints on the excitation. Exemplary constraints include a particular excitation k-space trajectory duration (for example, 5 milliseconds) and a particular RF excitation field fidelity (for example, a normalized root-mean-square error of 20 percent).
One current method for the joint design of an excitation k-space trajectory and corresponding RF excitation pulse is the 2D spiral trajectory optimization method described by Y. S. Levin, et al., in “Trajectory Optimization For Variable-Density Spiral Two-Dimensional Excitation,” Proc. Int. Soc. for Magn. Reson. Med. (ISMRM), 2006; 3012. This method focuses on optimizing 2D spiral trajectories, and is therefore limited in at least three ways. First, the method can only optimize over a specific class of spiral trajectories that consists of concentric rings. Second, the method and its underlying theory apply only to 2D radially-symmetric excitation patterns. Lastly, the method is limited to optimizing over 2D k-space and thus does not apply to often desirable three-dimensional (“3D”) excitations. The latter two limitations are hindering because they imply that the method is incapable of being used to excite many commonly-desired spatially-tailored patterns, such as a 2D square, a 3D box, or a thin slice. Additionally, the method provided by Levin is not applicable to parallel transmission coil arrays, but is instead limited to conventional systems.
Another current method for the joint design of an excitation k-space trajectory and corresponding RF excitation pulse is the echo-planar trajectory optimization method described by C. Y. Yip, et al., in “Joint Design of Trajectory and RF Pulses for Parallel Excitation,” Magn. Reson. Med., 2007; 58(3):598-604. This method focuses solely on the optimization of 2D echo-planar trajectories. Unlike the aforementioned method of Levin, this method is applicable to a general 2D excitation pattern and, therefore, radial symmetry of the desired excitation pattern is no longer a strict requirement. However, this technique is limited in that it optimizes only 2D echo-planar trajectories, and it thus limited in its application. First, it cannot be used to excite commonly-used 3D patterns, such as thin slices. Second, traversing echo-planar trajectories can result in lengthy, impractical durations of time because echo-planar traversals are limited by the maximum amplitude and slew rates of the gradient system of the MRI system. Also, when 2D echo-planar trajectories and waveforms are applied in the presence of inhomogeneities in the MRI system, they may cause the produced excitation to exhibit worse artifacts than other excitation patterns.
It would therefore be desirable to provide a method for the joint calculation of an excitation k-space trajectory and corresponding RF excitation pulse that is applicable to any arbitrary trajectory shape, including one-, two-, and three-dimensional trajectories. In addition, it would be desirable for such a method to be applicable not only to conventional MRI systems, but also to those that employ parallel transmission RF coils.